Quantum Statistics and Spacetime Surgery

Juven Wang Institute for Advanced Study, Harvard University CMSA Xiao-Gang Wen Perimeter Institute for Theoretical Physics, MIT Shing-Tung Yau Harvard University CMSA

Publications of CMSA of Harvard mathscidoc:1702.38058

We apply the geometric-topology surgery theory on spacetime manifolds to study the constraints of quantum statistics data in 2+1 and 3+1 spacetime dimensions. First, we introduce the fusion data for worldline and worldsheet operators capable creating anyon excitations of particles and strings, well-defined in gapped states of matter with intrinsic topological orders. Second, we introduce the braiding statistics data of particles and strings, such as the geometric Berry matrices for particle-string Aharonov-Bohm and multi-loop adiabatic braiding process, encoded by submanifold linkings, in the closed spacetime 3-manifolds and 4-manifolds. Third, we derive new quantum surgery constraints analogous to Verlinde formula associating fusion and braiding statistics data via spacetime surgery, essential for defining the theory of topological orders, and potentially correlated to bootstrap boundary physics such as gapless modes, conformal field theories or quantum anomalies.
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@inproceedings{juvenquantum,
  title={Quantum Statistics and Spacetime Surgery},
  author={Juven Wang, Xiao-Gang Wen, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207235011664201280},
}
Juven Wang, Xiao-Gang Wen, and Shing-Tung Yau. Quantum Statistics and Spacetime Surgery. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207235011664201280.
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